Question : A boat can travel 5 km upstream in 15 minutes. If the ratio of the speed of the boat in still water to the speed of the stream is 6 : 1, then how much time will the boat take to cover 19.6 km downstream?
Option 1: 54 minutes
Option 2: 26 minutes
Option 3: 42 minutes
Option 4: 31 minutes
Correct Answer: 42 minutes
Solution :
Let's the speed of the boat in still water as $B$ and the speed of the stream as $S$
So, B : S = 6 : 1
Upstream speed = B - S
Downstream, speed = B + S
The boat can travel 5 km upstream in 15 minutes (0.25 hours)
⇒ B − S = $\frac{5}{0.25}$ = 20 km/hr
Now, B : S = 6 : 1
⇒ B = 6k and S = k
⇒ 6k − k = 20 Km/hr
⇒ k = 4
speed downstream (B + S) = 24 + 4 = 28 km/h
⇒ Time = $\frac{\text{Distance}}{\text{SpeedTime}}$ = $\frac{19.6}{28}$
= 0.7 hours
= 0.7 × 60 minutes
= 42 minutes
Hence, the correct answer is 42 minutes.
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